Question
Case 2: Tesla Tesla manufactures cars in three plants and then ships them to four regions of the country as follows: Region 1 Region 2
Case 2: Tesla
Tesla manufactures cars in three plants and then ships them to four regions of the country as follows:
Region 1 | Region 2 | Region 3 | Region 4 | Capacity | |
Plant 1 | $131 | $218 | $266 | $120 | 450 |
Plant 2 | $250 | $116 | $263 | $278 | 600 |
Plant 3 | $178 | $132 | $122 | $180 | 500 |
Demand | 450 | 200 | 300 | 300 |
A plant's capacity is listed in the rightmost column, while a regions demand is represented in the bottom
row. The unit costs to ship one vehicle from each plant to each region are listed in the middle.
Part A. Develop an LP optimization model that finds the cheapest way of shipping the automobiles from
the plants to the regions that stays within the plant's capacities while also meeting regional demands.
Part B. Elon Musk would like to extend the capabilities of the initial baseline model to more closely reflect the specifics of the actual situation. Since unit production costs vary from plant to plant, and the selling prices vary across the regions, there are different after tax profit implications associated with where the car is produced and sold, and where it is ultimately shipped to.
Unit Production Cost | Tax Rate | |
Plant 1 | $14,350 | 30% |
Plant 2 | $16,270 | 35% |
Plant 3 | $16,940 | 22% |
Unit Selling Price | |
Region 1 | $19,290 |
Region 2 | $20,520 |
Region 3 | $17,570 |
Region 4 | $18,320 |
For example, if Plant 1 produces an auto and ships it to Region 2, the before tax profit will be the unit's selling price in the Region, less the production costs from the Plant, less the shipping costs from the Plant to the Region (= $20,520 - $14,350 - $218 = $5,952). Since it was produced at Plant 1, the applicable after-tax profit would be; $5,952*(1-30%) = $4,166.40
Enhance the previous Model from Part A to consider the objective of maximizing after-tax profits. How does the enhancement of the model impact the solution recommendations.
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